In an interference pattern, the ratio of intensity of two waves is $\frac{9}{25}$, then the ratio of maximum intensity to minimum intensity is:

16 : 1

Let Intensity of two waves are 9I and 25I.

$\text{Since } I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2 , I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2 $

$\Rightarrow I_{max} = (\sqrt {9I} + \sqrt {25I})^2 = 64I$

$\Rightarrow I_{min} =(\sqrt {25I} - \sqrt {9I})^2 = 4I$

$\frac{I_{max}}{I_{min}} = 16:1$